When China’s Lenovo Group Ltd. took over fading mobile-phone pioneer Motorola Mobility in October 2014, Chief Executive Yang Yuanqing vowed to restore the brand as a global leader.

Addressing staff at Motorola’s Chicago headquarters after the $2.91 billion deal closed, Mr. Yang told them their talents would propel the combined company to global dominance, recall several people who heard him. Together, he noted, the two companies already constituted the world’s third-biggest smartphone maker by shipments.